Grzegorz Kawiecki

Grzegorz Kawiecki OTHER RESEARCH ACTIVITIES 3. Bilinear Finite Element Formulation Applied to Helicopter Rotor Dynamics. A time finite element method based on Hamilton's Law of Varying Action was applied to the analysis of helicopter blade dynamics. The bilinear formulation of Hamilton's Law of Varying Action was used to discretize the temporal dependence of the equations of motion. Variable-order shape and test functions based on Legendre polynomials were used. Two approaches for the numerical implementation of the bilinear formulation were employed. One approach obtains the response of a general dynamic system using marching in time. The other approach is based on the assumption that the solution is identical at the beginning and end of one period. Therefore, this approach is suitable for periodic systems. The bilinear formulation in imposed periodicity mode is used to compute the response of a rigid blade with flap and lag degrees of freedom in forward flight. The bilinear formulation in marching mode was applied to find the Floquet transition matrix necessary to test the stability of blade motion.

Fig. 1 Blade equilibrium position, m = 0.4.

Fig. 2 Comparison of the results of stability analysis using the bilinear approach with published results.

For details see:

Kawiecki, G. and Sivaneri, N. T., "Bilinear Formulation Applied to the Response and Stability of Helicopter Rotor Blade," American Institute of Aeronautics and Astronautics Journal, Vol. 32, No. 10, pp. 2036 - 2043, October 1994.